Abstract Algebra

Problems taken from Chapter 4 - Cyclic Groups.

Problems

1. Problem 5 - Instead of ${\mathbb{Z}}_{18}$, do this for ${\mathbb{Z}}_{12}$.
2. Problem 9
3. Problem 14
4. Problem 23 - Skip part (a) since we did this in class.
5. Problem 24 - Hint: See Corollary 4.14. Your answer should be in terms of $p$ and $q$. Try this for small $p$ and $q$ to get an idea of the general method.
6. Problem 32 - This should not take you long; if it is then review the main theorems in this chapter.
7. Problem 39 - If $d\mid m$ then $m=d\cdot k$ for some integer $k\in \mathbb{N}$. If $g$ is a generator of $G$ then consider $g^k$.